Strong asymptotic freeness for free orthogonal quantum groups

Abstract

We prove that the normalized standard generators of the free orthogonal quantum group $O_N^{+}$ converge strongly to a free semicircular system as $N\to \infty$. Analogous results are obtained for the free unitary quantum groups, and some applications are given.

References in corpus (3)

• The Property of Rapid Decay for Discrete Quantum Groups
• Examples of factors which have no Cartan subalgebras
• Spectral analysis of the free orthogonal matrix

Cited by in corpus (5)

• The Connes embedding property for quantum group von Neumann algebras
• Orthogonal free quantum group factors are strongly 1-bounded
• Property RD and hypercontractivity for orthogonal free quantum groups
• Strong 1-Boundedness of Unimodular Free Orthogonal Quantum Groups
• Entropic uncertainty relations under localizations on discrete quantum groups